I have to disagree with you here; it's ideology, not economics.
The military is not having problems getting people specifically into combat arms, consequently opening those fields up for women is not gaining an economic advantage.
I can't quote numbers here, but I don't think too many people walk into the recruiter's office and say, "yeah, I'd like to join the Army/Navy/Marines/Air Force, I couldn't care less what job I have, just sign me up for something." People ship to boot camp with a specific job already lined up.
There are jobs where they have problems keeping manning levels up. For instance, the Navy has trouble recruiting and retaining people to operate nuclear reactors. But I don't think the Infantry has nearly the same problem.
I don't know what the latest quarterly figures are, but the military was paying very high re-enlistment bonuses; there was a cost to the high retention rates. In addition, as of October 2012, there have been more deaths in the Army due to suicide than to combat.
There is no question that the frequent rotations of troops in and out of the combat zones is taking its toll; bringing women into the combat arms fields would eliminate this pressure (by adding a larger pool of people to choose from). (It will open up a whole new can of worms, but that's a different subject.)
I have no doubt that feminists are pushing this as well, but as I said before when I referred to the Navy and the manpower shortages they faced some twenty years ago, I think the main reason the military is considering this is because of the manpower pressure.
Every sociologist in the world will tell you that this is a really stupid idea, but I think the powers that be have only stupid ideas left to choose from.